Math Problem Statement

Divide. Write your answer in scientific notation. (6 × 10^8) / (3 × 10^4)

Solution

To solve the problem 6×1083×104\frac{6 \times 10^8}{3 \times 10^4}, we will divide both the coefficients and the powers of 10.

Step 1: Divide the coefficients

63=2\frac{6}{3} = 2

Step 2: Subtract the exponents (using the property of exponents 10a10b=10ab\frac{10^a}{10^b} = 10^{a-b}):

108÷104=1084=10410^8 \div 10^4 = 10^{8-4} = 10^4

Final Answer:

2×1042 \times 10^4

So, the answer is 2×1042 \times 10^4 in scientific notation.

Would you like further explanation or have any questions?

Related Questions:

  1. How would you handle this if one of the numbers was negative?
  2. What would the answer be if the exponent on the denominator was higher than in the numerator?
  3. How do you convert from scientific notation to standard form?
  4. What other operations, besides division, can be applied using scientific notation?
  5. How can you simplify expressions that have multiple powers of 10?

Tip: Always remember to handle the coefficients and powers separately when working with scientific notation!

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Division of Exponents
Exponents Properties

Formulas

a × 10^m / b × 10^n = (a/b) × 10^(m-n)

Theorems

Properties of Exponents

Suitable Grade Level

Grades 7-9